Abstract

Synchronization of neural activity from distant parts of the brain is crucial for
the coordination of cognitive activities. Because neural synchronization varies both
in time and frequency, time–frequency (T-F) coherence is commonly employed to assess
interdependences in electrophysiological recordings. T-F coherence entails smoothing
the cross and power spectra to ensure statistical consistency of the estimate, which
reduces its T-F resolution. This trade-off has been described in detail when the cross
and power spectra are smoothed using identical smoothing operators, which may yield
spurious coherent frequencies. In this article, we examine the use of non-identical
smoothing operators for the estimation of T-F interdependence, i.e., phase synchronization
is characterized by phase locking between signals captured by the cross spectrum and
we may hence improve the trade-off by selectively smoothing the auto spectra. We first
show that the frequency marginal density of the present estimate is bound within [0,1]
when using non-identical smoothing operators. An analytic calculation of the bias
and variance of present estimators is performed and compared with the bias and variance
of standard T-F coherence using Monte Carlo simulations. We then test the use of non-identical
smoothing operators on simulated data, whose T-F properties are known through construction.
Finally, we analyze empirical data from eyes-closed surface electroencephalography
recorded in human subjects to investigate alpha-band synchronization. These analyses
show that selectively smoothing the auto spectra reduces the bias of the estimator
and may improve the detection of T-F interdependence in electrophysiological data
at high temporal resolution.